On correctness of the problems of nonlinear regression in case of monitoring natural and man-made objects
© Mostovoy V.S., Mostovoy S.V.
Under consideration there is a compliance with observed data and nonlinear models of monitoring. These models are
based on superposition of oscillators with free parameters. Optimal estimation of free parameters of model which enter into
model both linearly and nonlinearly, we shall consider as a problem of nonlinear regression. The optimality is understood in
sense of a global minimum of an objective functional. The point in space of possible values of free parameters of model in
which criterion has a global minimum is accepted as the optimal solution of a problem. For the chosen nonlinear mathematical
models it is necessary to find out the questions connected with existence of the solution, its uniqueness, and stability of
the solution depending on initial data. The last circumstance is especially important, as the algorithms constructed on the
basis of these models, are concentrated on direct processing of field supervision. It means dependence on characteristics
of the measuring equipment, errors of measurement and to accompanying by background noises. Separation of linear and
nonlinear parameters with the purpose of calculation process optimization is offered for construction of optimal estimations
model parameters. By search quasi-optimal solutions such division allows to use for the Monte-Carlo technique simulation
only nonlinear parameters. Linearly entering parameters are defined by the solution of system of the linear equations. Thus,
dimension of a search problem of optimal estimations is decreased on a size of a linear parameters vector dimension.